Taylor series expansion for evaluating the bounds of electric potentials in an electrostatic system with interval parameters. Issue 2 (5th March 2018) - Wang, Pengbo; Wang, Jingxuan
Abstract : Purpose: Uncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as interval numbers. The prediction of upper and lower bounds of the response of a system including uncertain parameters is of immense significance in uncertainty analysis. This paper aims to evaluate the upper and lower bounds of electric potentials in an electrostatic system efficiently with interval parameters. Design/methodology/approach: The Taylor series expansion is proposed for evaluating the upper and lower bounds of electric potentials in an electrostatic system with interval parameters. The uncertain parameters of the electrostatic system are represented by interval notations. By performing Taylor series expansion on the electric potentials obtained using the equilibrium governing equation and by using the properties of interval mathematics, the upper and lower bounds of the electric potentials of an electrostatic system can be calculated. Findings: To evaluate the accuracy and efficiency of the proposed method, the upper and lower bounds of the electric potentials and the computation time of the proposed method are compared with those obtained using the Monte Carlo simulation, which is referred to as a reference solution. Numerical examples illustrate that the bounds of electric potentials of this method are consistent with those obtained using the Monte Carlo simulation. Moreover, the proposed method is significantly more time-saving. Originality/value: This paper provides a rapid computational method to estimate the upper and lower bounds of electric potentials in electrostatics analysis with interval parameters. The precision of the proposed method is acceptable for engineering applications, and the computation time of the proposed method is significantly less than that of the Monte Carlo simulation, which is the most widely used method related to uncertainties. The Monte Carlo simulation requires a large number of samplings, and this leads to significant runtime consumption.